Solve sqrt{0.09*0.91/1400}

$$\sqrt{ \frac{ 0.09 \cdot 0.91 }{ 1400 } }$$

Evaluate

$$\frac{3\sqrt{26}}{2000}\approx 0.007648529$$

Solution Steps

Multiply 0.09 and 0.91 to get 0.0819.

$$\sqrt{\frac{0.0819}{1400}}$$

Expand \frac{0.0819}{1400} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{819}{14000000}}$$

Reduce the fraction \frac{819}{14000000} to lowest terms by extracting and canceling out 7.

$$\sqrt{\frac{117}{2000000}}$$

Rewrite the square root of the division \sqrt{\frac{117}{2000000}} as the division of square roots \frac{\sqrt{117}}{\sqrt{2000000}}.

$$\frac{\sqrt{117}}{\sqrt{2000000}}$$

Factor 117=3^{2}\times 13. Rewrite the square root of the product \sqrt{3^{2}\times 13} as the product of square roots \sqrt{3^{2}}\sqrt{13}. Take the square root of 3^{2}.

$$\frac{3\sqrt{13}}{\sqrt{2000000}}$$

Factor 2000000=1000^{2}\times 2. Rewrite the square root of the product \sqrt{1000^{2}\times 2} as the product of square roots \sqrt{1000^{2}}\sqrt{2}. Take the square root of 1000^{2}.

$$\frac{3\sqrt{13}}{1000\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{13}}{1000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{13}\sqrt{2}}{1000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{13}\sqrt{2}}{1000\times 2}$$

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{26}}{1000\times 2}$$

Multiply 1000 and 2 to get 2000.

$$\frac{3\sqrt{26}}{2000}$$